How do you manage VTE in the setting of persistent severe thrombocytopenia?

The thrombosis versus bleeding risk ratio should be weighed. The risk of VTE recurrence or propagation is highest in the first 30 days and we know that thrombocytopenia does not attenuate this risk. Providers should favor anticoagulation. In the case of cancer-associated thrombosis and chemotherapy-induced thrombocytopenia (where there is a high thrombosis risk and a usual expectation for platelet recovery), I would often be inclined to anticoagulate.

In terms of the practical management of an acute cancer-associated VTE, especially one with high-risk features (symptomatic PE, proximal DVT, or history of recurrent/progressive thrombosis), I would start therapeutic dose anticoagulation and attempt to maintain a platelet count close to 50,000 ...

Yes, with plt support (for transient thrombocytopenia). Plt threshold for transfusion at 50k.

It may be a good idea to estimate the risk of bleeding as well as the risk of further thrombosis. If thrombocytopenia is temporary, platelet transfusion and anticoagulation. If thrombocytopenia is going to last for a while and the count is expected to stay less than 50K, I would place a filter and hold all anticoagulation. If the count improves to better than 50K, low dose Lovenox may be considered after filter placement.